It concerns, more particularly, a pinion gearbox, as described, for example, in document U.S. Pat. No. 4,640,141, in a transversal position comprising a transmission input shaft and an output shaft mounted mutually parallel in the gearbox housing and comprising several pairs of engaged pinions to shift on a corresponding number of headway transmission ratios, and a reverse gear axle, parallel to the transmission input and output shafts, whereon are arranged (a) two idler wheels, rotating freely against each other whereof one is engaged in a fixed pinion on the transmission input shaft and the other is engaged in a fixed pinion on the output shaft, and (b) a synchronizing device arranged between the idler wheels ensuring between them a permanent connection.
Such a gearbox design has the advantage of not being very cumbersome for a gearbox consisting of two main shafts. However, the reverse synchronizing devices known to date and of such a design are either fast but too cumbersome, or not very cumbersome but not fast enough, or yet fast and not very cumbersome but with significant effect at the clutch level and a high level of noise.